<!doctype html>
<html>
<head>
<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>

<style type='text/css'>html {overflow-x: initial !important;}:root { --bg-color:#ffffff; --text-color:#333333; --select-text-bg-color:#B5D6FC; --select-text-font-color:auto; --monospace:"Lucida Console",Consolas,"Courier",monospace; --title-bar-height:20px; }
.mac-os-11 { --title-bar-height:28px; }
html { font-size: 14px; background-color: var(--bg-color); color: var(--text-color); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; -webkit-font-smoothing: antialiased; }
body { margin: 0px; padding: 0px; height: auto; inset: 0px; font-size: 1rem; line-height: 1.42857; overflow-x: hidden; background: inherit; tab-size: 4; }
iframe { margin: auto; }
a.url { word-break: break-all; }
a:active, a:hover { outline: 0px; }
.in-text-selection, ::selection { text-shadow: none; background: var(--select-text-bg-color); color: var(--select-text-font-color); }
#write { margin: 0px auto; height: auto; width: inherit; word-break: normal; overflow-wrap: break-word; position: relative; white-space: normal; overflow-x: visible; padding-top: 36px; }
#write.first-line-indent p { text-indent: 2em; }
#write.first-line-indent li p, #write.first-line-indent p * { text-indent: 0px; }
#write.first-line-indent li { margin-left: 2em; }
.for-image #write { padding-left: 8px; padding-right: 8px; }
body.typora-export { padding-left: 30px; padding-right: 30px; }
.typora-export .footnote-line, .typora-export li, .typora-export p { white-space: pre-wrap; }
.typora-export .task-list-item input { pointer-events: none; }
@media screen and (max-width: 500px) {
  body.typora-export { padding-left: 0px; padding-right: 0px; }
  #write { padding-left: 20px; padding-right: 20px; }
  .CodeMirror-sizer { margin-left: 0px !important; }
  .CodeMirror-gutters { display: none !important; }
}
#write li > figure:last-child { margin-bottom: 0.5rem; }
#write ol, #write ul { position: relative; }
img { max-width: 100%; vertical-align: middle; image-orientation: from-image; }
button, input, select, textarea { color: inherit; font: inherit; }
input[type="checkbox"], input[type="radio"] { line-height: normal; padding: 0px; }
*, ::after, ::before { box-sizing: border-box; }
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p, #write pre { width: inherit; }
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p { position: relative; }
p { line-height: inherit; }
h1, h2, h3, h4, h5, h6 { break-after: avoid-page; break-inside: avoid; orphans: 4; }
p { orphans: 4; }
h1 { font-size: 2rem; }
h2 { font-size: 1.8rem; }
h3 { font-size: 1.6rem; }
h4 { font-size: 1.4rem; }
h5 { font-size: 1.2rem; }
h6 { font-size: 1rem; }
.md-math-block, .md-rawblock, h1, h2, h3, h4, h5, h6, p { margin-top: 1rem; margin-bottom: 1rem; }
.hidden { display: none; }
.md-blockmeta { color: rgb(204, 204, 204); font-weight: 700; font-style: italic; }
a { cursor: pointer; }
sup.md-footnote { padding: 2px 4px; background-color: rgba(238, 238, 238, 0.7); color: rgb(85, 85, 85); border-radius: 4px; cursor: pointer; }
sup.md-footnote a, sup.md-footnote a:hover { color: inherit; text-transform: inherit; text-decoration: inherit; }
#write input[type="checkbox"] { cursor: pointer; width: inherit; height: inherit; }
figure { overflow-x: auto; margin: 1.2em 0px; max-width: calc(100% + 16px); padding: 0px; }
figure > table { margin: 0px; }
tr { break-inside: avoid; break-after: auto; }
thead { display: table-header-group; }
table { border-collapse: collapse; border-spacing: 0px; width: 100%; overflow: auto; break-inside: auto; text-align: left; }
table.md-table td { min-width: 32px; }
.CodeMirror-gutters { border-right: 0px; background-color: inherit; }
.CodeMirror-linenumber { user-select: none; }
.CodeMirror { text-align: left; }
.CodeMirror-placeholder { opacity: 0.3; }
.CodeMirror pre { padding: 0px 4px; }
.CodeMirror-lines { padding: 0px; }
div.hr:focus { cursor: none; }
#write pre { white-space: pre-wrap; }
#write.fences-no-line-wrapping pre { white-space: pre; }
#write pre.ty-contain-cm { white-space: normal; }
.CodeMirror-gutters { margin-right: 4px; }
.md-fences { font-size: 0.9rem; display: block; break-inside: avoid; text-align: left; overflow: visible; white-space: pre; background: inherit; position: relative !important; }
.md-fences-adv-panel { width: 100%; margin-top: 10px; text-align: center; padding-top: 0px; padding-bottom: 8px; overflow-x: auto; }
#write .md-fences.mock-cm { white-space: pre-wrap; }
.md-fences.md-fences-with-lineno { padding-left: 0px; }
#write.fences-no-line-wrapping .md-fences.mock-cm { white-space: pre; overflow-x: auto; }
.md-fences.mock-cm.md-fences-with-lineno { padding-left: 8px; }
.CodeMirror-line, twitterwidget { break-inside: avoid; }
.footnotes { opacity: 0.8; font-size: 0.9rem; margin-top: 1em; margin-bottom: 1em; }
.footnotes + .footnotes { margin-top: 0px; }
.md-reset { margin: 0px; padding: 0px; border: 0px; outline: 0px; vertical-align: top; background: 0px 0px; text-decoration: none; text-shadow: none; float: none; position: static; width: auto; height: auto; white-space: nowrap; cursor: inherit; -webkit-tap-highlight-color: transparent; line-height: normal; font-weight: 400; text-align: left; box-sizing: content-box; direction: ltr; }
li div { padding-top: 0px; }
blockquote { margin: 1rem 0px; }
li .mathjax-block, li p { margin: 0.5rem 0px; }
li blockquote { margin: 1rem 0px; }
li { margin: 0px; position: relative; }
blockquote > :last-child { margin-bottom: 0px; }
blockquote > :first-child, li > :first-child { margin-top: 0px; }
.footnotes-area { color: rgb(136, 136, 136); margin-top: 0.714rem; padding-bottom: 0.143rem; white-space: normal; }
#write .footnote-line { white-space: pre-wrap; }
@media print {
  body, html { border: 1px solid transparent; height: 99%; break-after: avoid; break-before: avoid; font-variant-ligatures: no-common-ligatures; }
  #write { margin-top: 0px; padding-top: 0px; border-color: transparent !important; }
  .typora-export * { -webkit-print-color-adjust: exact; }
  .typora-export #write { break-after: avoid; }
  .typora-export #write::after { height: 0px; }
  .is-mac table { break-inside: avoid; }
  .typora-export-show-outline .typora-export-sidebar { display: none; }
}
.footnote-line { margin-top: 0.714em; font-size: 0.7em; }
a img, img a { cursor: pointer; }
pre.md-meta-block { font-size: 0.8rem; min-height: 0.8rem; white-space: pre-wrap; background: rgb(204, 204, 204); display: block; overflow-x: hidden; }
p > .md-image:only-child:not(.md-img-error) img, p > img:only-child { display: block; margin: auto; }
#write.first-line-indent p > .md-image:only-child:not(.md-img-error) img { left: -2em; position: relative; }
p > .md-image:only-child { display: inline-block; width: 100%; }
#write .MathJax_Display { margin: 0.8em 0px 0px; }
.md-math-block { width: 100%; }
.md-math-block:not(:empty)::after { display: none; }
.MathJax_ref { fill: currentcolor; }
[contenteditable="true"]:active, [contenteditable="true"]:focus, [contenteditable="false"]:active, [contenteditable="false"]:focus { outline: 0px; box-shadow: none; }
.md-task-list-item { position: relative; list-style-type: none; }
.task-list-item.md-task-list-item { padding-left: 0px; }
.md-task-list-item > input { position: absolute; top: 0px; left: 0px; margin-left: -1.2em; margin-top: calc(1em - 10px); border: none; }
.math { font-size: 1rem; }
.md-toc { min-height: 3.58rem; position: relative; font-size: 0.9rem; border-radius: 10px; }
.md-toc-content { position: relative; margin-left: 0px; }
.md-toc-content::after, .md-toc::after { display: none; }
.md-toc-item { display: block; color: rgb(65, 131, 196); }
.md-toc-item a { text-decoration: none; }
.md-toc-inner:hover { text-decoration: underline; }
.md-toc-inner { display: inline-block; cursor: pointer; }
.md-toc-h1 .md-toc-inner { margin-left: 0px; font-weight: 700; }
.md-toc-h2 .md-toc-inner { margin-left: 2em; }
.md-toc-h3 .md-toc-inner { margin-left: 4em; }
.md-toc-h4 .md-toc-inner { margin-left: 6em; }
.md-toc-h5 .md-toc-inner { margin-left: 8em; }
.md-toc-h6 .md-toc-inner { margin-left: 10em; }
@media screen and (max-width: 48em) {
  .md-toc-h3 .md-toc-inner { margin-left: 3.5em; }
  .md-toc-h4 .md-toc-inner { margin-left: 5em; }
  .md-toc-h5 .md-toc-inner { margin-left: 6.5em; }
  .md-toc-h6 .md-toc-inner { margin-left: 8em; }
}
a.md-toc-inner { font-size: inherit; font-style: inherit; font-weight: inherit; line-height: inherit; }
.footnote-line a:not(.reversefootnote) { color: inherit; }
.md-attr { display: none; }
.md-fn-count::after { content: "."; }
code, pre, samp, tt { font-family: var(--monospace); }
kbd { margin: 0px 0.1em; padding: 0.1em 0.6em; font-size: 0.8em; color: rgb(36, 39, 41); background: rgb(255, 255, 255); border: 1px solid rgb(173, 179, 185); border-radius: 3px; box-shadow: rgba(12, 13, 14, 0.2) 0px 1px 0px, rgb(255, 255, 255) 0px 0px 0px 2px inset; white-space: nowrap; vertical-align: middle; }
.md-comment { color: rgb(162, 127, 3); opacity: 0.6; font-family: var(--monospace); }
code { text-align: left; vertical-align: initial; }
a.md-print-anchor { white-space: pre !important; border-width: initial !important; border-style: none !important; border-color: initial !important; display: inline-block !important; position: absolute !important; width: 1px !important; right: 0px !important; outline: 0px !important; background: 0px 0px !important; text-decoration: initial !important; text-shadow: initial !important; }
.os-windows.monocolor-emoji .md-emoji { font-family: "Segoe UI Symbol", sans-serif; }
.md-diagram-panel > svg { max-width: 100%; }
[lang="flow"] svg, [lang="mermaid"] svg { max-width: 100%; height: auto; }
[lang="mermaid"] .node text { font-size: 1rem; }
table tr th { border-bottom: 0px; }
video { max-width: 100%; display: block; margin: 0px auto; }
iframe { max-width: 100%; width: 100%; border: none; }
.highlight td, .highlight tr { border: 0px; }
mark { background: rgb(255, 255, 0); color: rgb(0, 0, 0); }
.md-html-inline .md-plain, .md-html-inline strong, mark .md-inline-math, mark strong { color: inherit; }
.md-expand mark .md-meta { opacity: 0.3 !important; }
mark .md-meta { color: rgb(0, 0, 0); }
@media print {
  .typora-export h1, .typora-export h2, .typora-export h3, .typora-export h4, .typora-export h5, .typora-export h6 { break-inside: avoid; }
}
.md-diagram-panel .messageText { stroke: none !important; }
.md-diagram-panel .start-state { fill: var(--node-fill); }
.md-diagram-panel .edgeLabel rect { opacity: 1 !important; }
.md-fences.md-fences-math { font-size: 1em; }
.md-fences-advanced:not(.md-focus) { padding: 0px; white-space: nowrap; border: 0px; }
.md-fences-advanced:not(.md-focus) { background: inherit; }
.typora-export-show-outline .typora-export-content { max-width: 1440px; margin: auto; display: flex; flex-direction: row; }
.typora-export-sidebar { width: 300px; font-size: 0.8rem; margin-top: 80px; margin-right: 18px; }
.typora-export-show-outline #write { --webkit-flex:2; flex: 2 1 0%; }
.typora-export-sidebar .outline-content { position: fixed; top: 0px; max-height: 100%; overflow: hidden auto; padding-bottom: 30px; padding-top: 60px; width: 300px; }
@media screen and (max-width: 1024px) {
  .typora-export-sidebar, .typora-export-sidebar .outline-content { width: 240px; }
}
@media screen and (max-width: 800px) {
  .typora-export-sidebar { display: none; }
}
.outline-content li, .outline-content ul { margin-left: 0px; margin-right: 0px; padding-left: 0px; padding-right: 0px; list-style: none; }
.outline-content ul { margin-top: 0px; margin-bottom: 0px; }
.outline-content strong { font-weight: 400; }
.outline-expander { width: 1rem; height: 1.42857rem; position: relative; display: table-cell; vertical-align: middle; cursor: pointer; padding-left: 4px; }
.outline-expander::before { content: ""; position: relative; font-family: Ionicons; display: inline-block; font-size: 8px; vertical-align: middle; }
.outline-item { padding-top: 3px; padding-bottom: 3px; cursor: pointer; }
.outline-expander:hover::before { content: ""; }
.outline-h1 > .outline-item { padding-left: 0px; }
.outline-h2 > .outline-item { padding-left: 1em; }
.outline-h3 > .outline-item { padding-left: 2em; }
.outline-h4 > .outline-item { padding-left: 3em; }
.outline-h5 > .outline-item { padding-left: 4em; }
.outline-h6 > .outline-item { padding-left: 5em; }
.outline-label { cursor: pointer; display: table-cell; vertical-align: middle; text-decoration: none; color: inherit; }
.outline-label:hover { text-decoration: underline; }
.outline-item:hover { border-color: rgb(245, 245, 245); background-color: var(--item-hover-bg-color); }
.outline-item:hover { margin-left: -28px; margin-right: -28px; border-left: 28px solid transparent; border-right: 28px solid transparent; }
.outline-item-single .outline-expander::before, .outline-item-single .outline-expander:hover::before { display: none; }
.outline-item-open > .outline-item > .outline-expander::before { content: ""; }
.outline-children { display: none; }
.info-panel-tab-wrapper { display: none; }
.outline-item-open > .outline-children { display: block; }
.typora-export .outline-item { padding-top: 1px; padding-bottom: 1px; }
.typora-export .outline-item:hover { margin-right: -8px; border-right: 8px solid transparent; }
.typora-export .outline-expander::before { content: "+"; font-family: inherit; top: -1px; }
.typora-export .outline-expander:hover::before, .typora-export .outline-item-open > .outline-item > .outline-expander::before { content: "−"; }
.typora-export-collapse-outline .outline-children { display: none; }
.typora-export-collapse-outline .outline-item-open > .outline-children, .typora-export-no-collapse-outline .outline-children { display: block; }
.typora-export-no-collapse-outline .outline-expander::before { content: "" !important; }
.typora-export-show-outline .outline-item-active > .outline-item .outline-label { font-weight: 700; }
.md-inline-math-container mjx-container { zoom: 0.95; }



:root {
  --active-file-bg-color: #2c2b2b;
  --active-file-bg-color: rgba(32, 43, 51, 0.63);
  --active-file-text-color: white;
  --bg-color: #fff;
  --text-color: #333;
  --side-bar-bg-color: #f5f5f5;
  --control-text-color: #666;
}

/* 防止用户自定义背景颜色对网页的影响，添加让用户可以自定义字体 */
html {
  color: #333;
  background: #fff;
  -webkit-text-size-adjust: 100%;
  -ms-text-size-adjust: 100%;
  text-rendering: optimizelegibility;
  font-size: 14px;
  -webkit-font-smoothing: initial;
}

#write {
  max-width: 960px;
  padding-top: 2em;
  padding-left: 60px;
  padding-right: 60px;
  min-height: calc(100vh - 6em);
  -webkit-font-smoothing: antialiased;
  font-size: 16px;
}

.typora-node #write {
  min-height: calc(100% - 6em);
}

pre.md-meta-block {
  background: #f5f5f5;
  padding: 1em;
  border-radius: 3px;
  font-size: 14px;
}

@media screen and (max-width: 800px) {
    html {
      font-size: 14px;
    }

    #write {
      padding-left: 30px;
      padding-right: 30px;
      font-size: 14px;
    }
}

@media screen and (min-width: 1100px) {
    body, #footer-word-count-info {
      background: #f5f5f5;
    }

    body.pin-outline,
    .pin-outline #footer-word-count-info,
    .pin-outline footer {
      background: #fff;
    }

    #write {
      max-width: 1000px;
      padding: 40px 60px;
      background: #fff;
      margin: 3em auto 3em;
      border: 1px solid #ddd;
      border-width: 0 1px;
    }

    .pin-outline #write {
      max-width: 1000px;
      background: #fff;
      margin: 0 0 0;
      border: 0;
      padding-left: 60px;
      padding-right: 60px;
    }

    footer {
      background-color: transparent;
    }
}

@media screen and (min-width: 1300px) {
    body.pin-outline,
    .pin-outline #footer-word-count-info,
    .pin-outline footer {
      background: #f5f5f5;
    }

    .pin-outline  #write {
      max-width: 1000px;
      padding: 40px 60px;
      background: #fff;
      margin: 3em auto 3em;
      border: 1px solid #ddd;
      border-width: 0 1px;
    }

    .pin-outline footer {
      background-color: transparent;
    }

    #footer-word-count-info {
      background: #f5f5f5;
    }
}


/* 如果你的项目仅支持 IE9+ | Chrome | Firefox 等，推荐在 <html> 中添加 .borderbox 这个 class */
html.borderbox *, html.borderbox *:before, html.borderbox *:after {
  -moz-box-sizing: border-box;
  -webkit-box-sizing: border-box;
  box-sizing: border-box;
}

/* 内外边距通常让各个浏览器样式的表现位置不同 */
body, dl, dt, dd, ul, ol, li, h1, h2, h3, h4, h5, h6, code, form, fieldset, legend, input, textarea, p, blockquote, th, td, hr, button, article, aside, details, figcaption, figure, footer, header, menu, nav, section {
  margin: 0;
  padding: 0;
}

/* 重设 HTML5 标签, IE 需要在 js 中 createElement(TAG) */
article, aside, details, figcaption, figure, footer, header, menu, nav, section {
  display: block;
}

/* HTML5 媒体文件跟 img 保持一致 */
audio, canvas, video {
  display: inline-block;
}

/* 要注意表单元素并不继承父级 font 的问题 */
body, button, input, select, textarea {
  font: 300 1em/1.8 "PingFang SC", "Lantinghei SC", "Microsoft Yahei", "Hiragino Sans GB", "Microsoft Sans Serif", "WenQuanYi Micro Hei", sans;
}

body {
  font-family: "PingFang SC", "Lantinghei SC", "Microsoft Yahei", "Hiragino Sans GB", "Microsoft Sans Serif", "WenQuanYi Micro Hei", sans;
}

h1, h2, h3, h4, h5, h6 {
  font-family: "TimesNewRomanPS-ItalicMT", "PingFang SC", "Lantinghei SC", "Microsoft Yahei", "Hiragino Sans GB", "Microsoft Sans Serif", "WenQuanYi Micro Hei", sans;
  /*font-family: "PingFang SC", "Lantinghei SC", "Microsoft Yahei", "Hiragino Sans GB", "Microsoft Sans Serif", "WenQuanYi Micro Hei", sans;*/
  -webkit-font-smoothing: initial;
  font-weight: 100;
  color: var(--text-color);
  line-height: 1.35; 
  font-variant-numeric: lining-nums;
  margin-bottom: 1em;
}

em {
  font-family: Georgia-Italic, STSongti-SC-Light, serif;
}

strong em,
em strong {
  font-family: Georgia-BoldItalic, STSongti-SC-Regular, serif;
}

button::-moz-focus-inner,
input::-moz-focus-inner {
  padding: 0;
  border: 0;
}

/* 去掉各Table cell 的边距并让其边重合 */
table {
  border-collapse: collapse;
  border-spacing: 0;
}

/* 去除默认边框 */
fieldset, img {
  border: 0;
}

/* 块/段落引用 */
blockquote {
  position: relative;
  color: rgb(0, 0, 0);
  font-weight: 400;
  border-left: 4px solid #1abc9c;
  padding-left: 1.5em;
  margin: 1em 3em 1em 2em;
  background-color:rgb(131 232 194 / 14%);
}

@media only screen and ( max-width: 640px ) {
  blockquote {
    margin: 1em 0;
  }
}

/* Firefox 以外，元素没有下划线，需添加 */
acronym, abbr {
  border-bottom: 1px dotted;
  font-variant: normal;
}

/* 添加鼠标问号，进一步确保应用的语义是正确的（要知道，交互他们也有洁癖，如果你不去掉，那得多花点口舌） */
abbr {
  cursor: help;
}

address, caption, cite, code, dfn, th, var {
  font-style: normal;
  font-weight: 400;
}

/* 去掉列表前的标识, li 会继承，大部分网站通常用列表来很多内容，所以应该当去 */
ul, ol {
  list-style: none;
}

/* 对齐是排版最重要的因素, 别让什么都居中 */
caption, th {
  text-align: left;
}

q:before, q:after {
  content: '';
}

/* 统一上标和下标 */
sub, sup {
  font-size: 75%;
  line-height: 0;
  position: relative;
}

:root sub, :root sup {
  vertical-align: baseline; /* for ie9 and other modern browsers */
}

sup {
  top: -0.5em;
}

sub {
  bottom: -0.25em;
}

/* 让链接在 hover 状态下显示下划线 */
a {
  color: #1abc9c;
}

a:hover {
  text-decoration: underline;
}

#write a {
  border-bottom: 1px solid #1abc9c;
}

#write a:hover {
  border-bottom-color: #555;
  color: #555;
  text-decoration: none;
}

/* 默认不显示下划线，保持页面简洁 */
ins, a {
  text-decoration: none;
}

/* 标记，类似于手写的荧光笔的作用 */
mark {
  background: #fffdd1;
  border-bottom: 1px solid #ffedce;
  padding: 2px;
  margin: 0 5px;
}

/* 代码片断 */
pre, code, pre tt {
  font-family: Courier, 'Courier New', monospace;
}

#write .md-fences {
  border: 1px solid #ddd;
  padding: 1em 0.5em;
  display: block;
  -webkit-overflow-scrolling: touch;
}

/* 一致化 horizontal rule */
hr {
  border: none;
  border-bottom: 1px solid #cfcfcf;
  margin-bottom: 0.8em;
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<div id='write'  class=''><h1 id='第3章-多维随机变量及其分布'><span>第3章 多维随机变量及其分布</span></h1><h2 id='一二维随机变量'><span>一、二维随机变量</span></h2><h3 id='1定义'><span>1.定义 </span></h3><blockquote><p><span>设</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.729ex" height="1.538ex" role="img" focusable="false" viewBox="0 -680 764 680" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-26-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 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68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D446" xlink:href="#MJX-27-TEX-I-1D446"></use></g><g data-mml-node="mo" transform="translate(922.8,0)"><use data-c="3D" xlink:href="#MJX-27-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(1978.6,0)"><use data-c="7B" xlink:href="#MJX-27-TEX-N-7B"></use></g><g data-mml-node="mi" transform="translate(2478.6,0)"><use data-c="1D452" xlink:href="#MJX-27-TEX-I-1D452"></use></g><g data-mml-node="mo" transform="translate(2944.6,0)"><use data-c="7D" xlink:href="#MJX-27-TEX-N-7D"></use></g><g data-mml-node="mi" transform="translate(3444.6,0)"><text data-variant="italic" transform="scale(1,-1)" font-size="884px" font-family="serif" font-style="italic">，</text></g><g data-mml-node="mi" transform="translate(4328.3,0)"><use data-c="1D44B" xlink:href="#MJX-27-TEX-I-1D44B"></use></g><g data-mml-node="mo" transform="translate(5458.1,0)"><use data-c="3D" xlink:href="#MJX-27-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(6513.9,0)"><use data-c="1D44B" xlink:href="#MJX-27-TEX-I-1D44B"></use></g><g data-mml-node="mo" transform="translate(7365.9,0)"><use data-c="28" xlink:href="#MJX-27-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(7754.9,0)"><use data-c="1D452" xlink:href="#MJX-27-TEX-I-1D452"></use></g><g data-mml-node="mo" transform="translate(8220.9,0)"><use data-c="29" xlink:href="#MJX-27-TEX-N-29"></use></g><g data-mml-node="mtext" transform="translate(8609.9,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">和</text></g><g data-mml-node="mi" transform="translate(9493.6,0)"><use data-c="1D44C" xlink:href="#MJX-27-TEX-I-1D44C"></use></g><g data-mml-node="mo" transform="translate(10534.4,0)"><use data-c="3D" xlink:href="#MJX-27-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(11590.2,0)"><use data-c="1D44C" xlink:href="#MJX-27-TEX-I-1D44C"></use></g><g data-mml-node="mo" transform="translate(12353.2,0)"><use data-c="28" xlink:href="#MJX-27-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(12742.2,0)"><use data-c="1D452" xlink:href="#MJX-27-TEX-I-1D452"></use></g><g data-mml-node="mo" transform="translate(13208.2,0)"><use data-c="29" xlink:href="#MJX-27-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mo fence="false" stretchy="false">{</mo><mi>e</mi><mo fence="false" stretchy="false">}</mo><mi>，</mi><mi>X</mi><mo>=</mo><mi>X</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mtext>和</mtext><mi>Y</mi><mo>=</mo><mi>Y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">S=\{e\} ， X=X(e)  和  Y=Y(e)</script><span>是定义在 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.459ex" height="1.645ex" role="img" focusable="false" viewBox="0 -705 645 727" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-28-TEX-I-1D446" d="M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 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data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mtext>时</mtext><mi>，</mi><mtext>有</mtext><mi>F</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mi>F</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mi>F</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mi>F</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>≥</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">对于任意  \left(x_{1}, y_{1}\right) ，\left(x_{2}, y_{2}\right)  ，当  x_{1}<x_{2}, y_{1}<y_{2}  时，有
F\left(x_{2}, y_{2}\right)-F\left(x_{2}, y_{1}\right)-F\left(x_{1}, y_{2}\right)+F\left(x_{1}, y_{1}\right) \geq0</script></li></ul><p><img src="C:\Users\Administrator\AppData\Roaming\Typora\typora-user-images\image-20220414135858294.png" alt="image-20220414135858294" style="zoom: 33%;" /></p><h3 id='3二维离散随机变量'><span>3.二维</span><strong><span>离散</span></strong><span>随机变量</span></h3><blockquote><p><span>设二维随机变量  </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.42ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2837.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-47-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 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180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z"></path><path id="MJX-47-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><use data-c="28" xlink:href="#MJX-47-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(389,0)"><use data-c="1D44B" xlink:href="#MJX-47-TEX-I-1D44B"></use></g><g data-mml-node="mo" transform="translate(1241,0)"><use data-c="2C" xlink:href="#MJX-47-TEX-N-2C"></use></g><g data-mml-node="mi" transform="translate(1685.7,0)"><use data-c="1D44C" xlink:href="#MJX-47-TEX-I-1D44C"></use></g><g data-mml-node="mo" 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xlink:href="#MJX-47-TEX-I-1D44C"></use></g><g data-mml-node="mo" transform="translate(2448.7,0)"><use data-c="29" xlink:href="#MJX-47-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">(X, Y)</script><span>  为二维离散型随机变量.设二维离散型随机变量 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.42ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2837.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-41-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 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的概率分布或分布律</span></strong><span>，或随机变 量  </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.928ex" height="1.545ex" role="img" focusable="false" viewBox="0 -683 852 683" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-44-TEX-I-1D44B" d="M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 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aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-45-TEX-I-1D44C" d="M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D44C" xlink:href="#MJX-45-TEX-I-1D44C"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">Y </script><span> 的</span><strong><span>联合分布律.</span></strong></p></blockquote><h2 id='二边缘分布'><span>二、边缘分布</span></h2><h3 id='1离散随机变量'><span>1.</span><strong><span>离散</span></strong><span>随机变量</span></h3><blockquote><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="50.989ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 22537.3 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-46-TEX-I-1D443" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 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xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>X</mi><mo>.</mo></mrow></msub><mo>=</mo><msub><mi>F</mi><mi>X</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo><mo>,</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mo>.</mo><mi>Y</mi></mrow></msub><mo>=</mo><msub><mi>F</mi><mi>Y</mi></msub><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>y</mi><mo>,</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">P_{X.}=F_X(x)=F(x,+\infty),P_{.Y}=F_Y(y)=F(y,+\infty)</script><strong><span>注意上面的点</span></strong></p></blockquote><p><img src="C:\Users\Administrator\AppData\Roaming\Typora\typora-user-images\image-20220414141136311.png" alt="image-20220414141136311" style="zoom: 50%;" /></p><blockquote><p><span>联合分布律可以推出</span><code>边缘分布概率</code><span>，</span><strong><span>反之未然</span></strong><span>。</span></p></blockquote><h3 id='2连续随机变量'><span>2.</span><strong><span>连续</span></strong><span>随机变量</span></h3><blockquote><p><span>对于二维连续型随机变量</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.42ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2837.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-47-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-47-TEX-I-1D44B" d="M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 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